`A\ (6,3),\ B(-3,5),\ C(4,-2)\ a n d\ D(x ,3x)` are four points. If `"Delta"D B C :"Delta"A B C=1:2,` then `x` is equal to a. 11/8 b. 8/11 c. 3 d. none of these

Explanation

Given,


`A(6,3), B(-3,5), C(4,-2) \text { and } D(x, 3 x)`



By using area of triangle `=\frac{1}{2}|x_{1}(y_{2}-y_{3})+x_{2}(y_{3}-y_{2})+x_{3}(y_{1}-y_{2})|`


Area of `\triangle {DBC}=|\frac{({x})(5+2)+(-3)(-2-3 {x})+4(3 {x}-5)}{2}|=`
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